Question

State whether the statement given in the question is true or False:

If $\frac{p}{q}$ is a rational number and $m$ is a non-zero integer, then $\left(\frac{p}{q}\right)=\frac{(p\times m)}{(q\times m)}$is a rational number not equivalent to $\frac{p}{q}$.

• A. True
• B. False

Answer 1

The correct option is B False

Given : $\frac{p}{q}$is equivalent to $\left(\frac{p}{q}\right)=\frac{(p\times m)}{(q\times m)}$

we know that a fraction remains the same when the numerator and denominator are multiplied or divided by a same nonzero number.

So we have $\left(\frac{p}{q}\right)=\frac{(p\times m)}{(q\times m)}$which is a rational number equivalent to $\frac{p}{q}$.

Hence, the given statement is “False”.